Systems and methods for a wavelet transform viewer

ABSTRACT

Techniques for the display of a signal with a wavelet transform of that signal in a wavelet transform viewer are disclosed, according to embodiments. According to embodiments, the wavelet transform viewer can display a plot of physiological signals such as a photoplethysmograph (PPG) signal. A portion of the plot of the signal can be selected. A wavelet transform the selected portion of the signal can be calculated and a wavelet plot of the tranformed signal can be displayed simultaneously with that signal. A plot of the selected portion of the signal can also be simultaneously displayed with both the plot of the signal and the wavelet plot.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application No.61/077,072, filed Jun. 30, 2008 and U.S. Provisional Application No.61/077,130, filed Jun. 30, 2008, which are hereby incorporated byreference herein in their entireties.

SUMMARY

The present disclosure relates to a signal viewer and, moreparticularly, the present disclosure relates to a wavelet transformviewer for the simultaneous display of a signal with a wavelet transformof that signal.

In an embodiment, a wavelet transform viewer is provided that cansimultaneous display a signal and a wavelet transform of a portion ofthat signal. A signal is received and a portion of the signal isselected. The selected portion of the signal is transformed using awavelet transform to generate a transformed signal. A wavelet plot isgenerated based on the transformed signal and the wavelet plot isdisplayed with the signal.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other features of the present disclosure, its nature andvarious advantages will be more apparent upon consideration of thefollowing detailed description, taken in conjunction with theaccompanying drawings in which:

FIG. 1 shows an illustrative pulse oximetry system in accordance with anembodiment;

FIG. 2 is a block diagram of the illustrative pulse oximetry system ofFIG. 1 coupled to a patient in accordance with an embodiment;

FIGS. 3( a) and 3(b) show illustrative views of a scalogram derived froma PPG signal in accordance with an embodiment;

FIG. 3( c) shows an illustrative scalogram derived from a signalcontaining two pertinent components in accordance with an embodiment;

FIG. 3( d) shows an illustrative schematic of signals associated with aridge in FIG. 3( c) and illustrative schematics of a further waveletdecomposition of these newly derived signals in accordance with anembodiment;

FIGS. 3( e) and 3(f) are flow charts of illustrative steps involved inperforming an inverse continuous wavelet transform in accordance withembodiments;

FIG. 4 is a block diagram of an illustrative continuous waveletprocessing system that includes a wavelet transform viewer in accordancewith some embodiments; and

FIGS. 5-8 are illustrative displays of a wavelet transform viewer inaccordance with embodiments; and

FIG. 9 flowchart of an illustrative process for generating a wavelettransform viewer display in accordance with an embodiment.

DETAILED DESCRIPTION

An oximeter is a medical device that may determine the oxygen saturationof the blood. One common type of oximeter is a pulse oximeter, which mayindirectly measure the oxygen saturation of a patient's blood (asopposed to measuring oxygen saturation directly by analyzing a bloodsample taken from the patient) and changes in blood volume in the skin.Ancillary to the blood oxygen saturation measurement, pulse oximetersmay also be used to measure the pulse rate of the patient. Pulseoximeters typically measure and display various blood flowcharacteristics including, but not limited to, the oxygen saturation ofhemoglobin in arterial blood.

An oximeter may include a light sensor that is placed at a site on apatient, typically a fingertip, toe, forehead or earlobe, or in the caseof a neonate, across a foot. The oximeter may pass light using a lightsource through blood perfused tissue and photoelectrically sense theabsorption of light in the tissue. For example, the oximeter may measurethe intensity of light that is received at the light sensor as afunction of time. A signal representing light intensity versus time or amathematical manipulation of this signal (e.g., a scaled versionthereof, a log taken thereof, a scaled version of a log taken thereof,etc.) may be referred to as the photoplethysmograph (PPG) signal. Inaddition, the term “PPG signal,” as used herein, may also refer to anabsorption signal (i.e., representing the amount of light absorbed bythe tissue) or any suitable mathematical manipulation thereof. The lightintensity or the amount of light absorbed may then be used to calculatethe amount of the blood constituent (e.g., oxyhemoglobin) being measuredas well as the pulse rate and when each individual pulse occurs.

The light passed through the tissue is selected to be of one or morewavelengths that are absorbed by the blood in an amount representativeof the amount of the blood constituent present in the blood. The amountof light passed through the tissue varies in accordance with thechanging amount of blood constituent in the tissue and the related lightabsorption. Red and infrared wavelengths may be used because it has beenobserved that highly oxygenated blood will absorb relatively less redlight and more infrared light than blood with a lower oxygen saturation.By comparing the intensities of two wavelengths at different points inthe pulse cycle, it is possible to estimate the blood oxygen saturationof hemoglobin in arterial blood.

When the measured blood parameter is the oxygen saturation ofhemoglobin, a convenient starting point assumes a saturation calculationbased on Lambert-Beer's law. The following notation will be used herein:I(λ,t)=I _(o)(λ)exp(−(sβ _(o)(λ)+(1−s)β_(r)(λ))l(t))  (1)where:λ=wavelength;t=time;I=intensity of light detected;I_(o)=intensity of light transmitted;s=oxygen saturation;β_(o), β_(r)=empirically derived absorption coefficients; andl(t)=a combination of concentration and path length from emitter todetector as a function of time.

The traditional approach measures light absorption at two wavelengths(e.g., red and infrared (IR)), and then calculates saturation by solvingfor the “ratio of ratios” as follows.

1. First, the natural logarithm of (1) is taken (“log” will be used torepresent the natural logarithm) for IR and Redlog I=log I _(o)−(sβ _(o)+(1−s)β_(r))l  (2)2. (2) is then differentiated with respect to time

$\begin{matrix}{\frac{{\mathbb{d}\log}\; I}{\mathbb{d}t} = {{- \left( {{s\;\beta_{o}} + {\left( {1 - s} \right)\beta_{r}}} \right)}\frac{\mathbb{d}l}{\mathbb{d}t}}} & (3)\end{matrix}$3. Red (3) is divided by IR (3)

$\begin{matrix}{\frac{{\mathbb{d}\log}\;{{I\left( \lambda_{R} \right)}/{\mathbb{d}t}}}{{\mathbb{d}\log}\;{{I\left( \lambda_{IR} \right)}/{\mathbb{d}t}}} = \frac{{s\;{\beta_{o}\left( \lambda_{R} \right)}} + {\left( {1 - s} \right){\beta_{r}\left( \lambda_{R} \right)}}}{{s\;{\beta_{o}\left( \lambda_{IR} \right)}} + {\left( {1 - s} \right){\beta_{r}\left( \lambda_{IR} \right)}}}} & (4)\end{matrix}$4. Solving for s

$s = \frac{{\frac{{\mathbb{d}\log}\;{I\left( \lambda_{IR} \right)}}{\mathbb{d}t}{\beta_{r}\left( \lambda_{R} \right)}} - {\frac{{\mathbb{d}\log}\;{I\left( \lambda_{R} \right)}}{\mathbb{d}t}{\beta_{r}\left( \lambda_{IR} \right)}}}{\begin{matrix}{{\frac{{\mathbb{d}\log}\;{I\left( \lambda_{R} \right)}}{\mathbb{d}t}\left( {{\beta_{o}\left( \lambda_{IR} \right)} - {\beta_{r}\left( \lambda_{IR} \right)}} \right)} -} \\{\frac{{\mathbb{d}\log}\;{I\left( \lambda_{IR} \right)}}{\mathbb{d}t}\left( {{\beta_{o}\left( \lambda_{R} \right)} - {\beta_{r}\left( \lambda_{R} \right)}} \right)}\end{matrix}}$Note in discrete time

$\frac{{\mathbb{d}\log}\;{I\left( {\lambda,t} \right)}}{\mathbb{d}t} \simeq {{\log\;{I\left( {\lambda,t_{2}} \right)}} - {\log\;{I\left( {\lambda,t_{1}} \right)}}}$Using log A−log B=log A/B,

$\frac{{\mathbb{d}\log}\;{I\left( {\lambda,t} \right)}}{\mathbb{d}t} \simeq {\log\left( \frac{I\left( {t_{2},\lambda} \right)}{I\left( {t_{1},\lambda} \right)} \right)}$So, (4) can be rewritten as

$\begin{matrix}{{\frac{\frac{{\mathbb{d}\log}\;{I\left( \lambda_{R} \right)}}{\mathbb{d}t}}{\frac{{\mathbb{d}\log}\;{I\left( \lambda_{IR} \right)}}{\mathbb{d}t}} \simeq \frac{\log\left( \frac{I\left( {t_{1},\lambda_{R}} \right)}{I\left( {t_{2},\lambda_{R}} \right)} \right)}{\log\left( \frac{I\left( {t_{1},\lambda_{IR}} \right)}{I\left( {t_{2},\lambda_{IR}} \right)} \right)}} = R} & (5)\end{matrix}$where R represents the “ratio of ratios.” Solving (4) for s using (5)gives

$s = {\frac{{\beta_{r}\left( \lambda_{R} \right)} - {R\;{\beta_{r}\left( \lambda_{IR} \right)}}}{{R\left( {{\beta_{o}\left( \lambda_{IR} \right)} - {\beta_{r}\left( \lambda_{IR} \right)}} \right)} - {\beta_{o}\left( \lambda_{R} \right)} + {\beta_{r}\left( \lambda_{R} \right)}}.}$From (5), R can be calculated using two points (e.g., PPG maximum andminimum), or a family of points. One method using a family of pointsuses a modified version of (5). Using the relationship

$\begin{matrix}{\frac{{\mathbb{d}\log}\; I}{\mathbb{d}t} = \frac{{\mathbb{d}I}/{\mathbb{d}t}}{I}} & (6)\end{matrix}$now (5) becomes

$\begin{matrix}\begin{matrix}{\frac{\frac{{\mathbb{d}\log}\;{I\left( \lambda_{R} \right)}}{\mathbb{d}t}}{\frac{{\mathbb{d}\log}\;{I\left( \lambda_{IR} \right)}}{\mathbb{d}t}} \simeq \frac{\frac{{I\left( {t_{2},\lambda_{R}} \right)} - {I\left( {t_{1},\lambda_{R}} \right)}}{I\left( {t_{1},\lambda_{R}} \right)}}{\frac{{I\left( {t_{2},\lambda_{IR}} \right)} - {I\left( {t_{1},\lambda_{IR}} \right)}}{I\left( {t_{1},\lambda_{IR}} \right)}}} \\{= \frac{\left\lbrack {{I\left( {t_{2},\lambda_{IR}} \right)} - {I\left( {t_{1},\lambda_{IR}} \right)}} \right\rbrack{I\left( {t_{1},\lambda_{R}} \right)}}{\left\lbrack {{I\left( {t_{2},\lambda_{IR}} \right)} - {I\left( {t_{1},\lambda_{IR}} \right)}} \right\rbrack{I\left( {t_{1},\lambda_{R}} \right)}}} \\{= R}\end{matrix} & (7)\end{matrix}$which defines a cluster of points whose slope of y versus x will give Rwherex(t)=[I(t ₂,λ_(IR))−I(t ₁,λ_(IR))]I(t ₁,λ_(R))y(t)=[I(t ₂,λ_(R))−I(t ₁,λ_(R))]I(t ₁,λ_(IR))y(t)=Rx(t)  (8)

FIG. 1 is a perspective view of an embodiment of a pulse oximetry system10. System 10 may include a sensor 12 and a pulse oximetry monitor 14.Sensor 12 may include an emitter 16 for emitting light at two or morewavelengths into a patient's tissue. A detector 18 may also be providedin sensor 12 for detecting the light originally from emitter 16 thatemanates from the patient's tissue after passing through the tissue.

According to another embodiment and as will be described, system 10 mayinclude a plurality of sensors forming a sensor array in lieu of singlesensor 12. Each of the sensors of the sensor array may be acomplementary metal oxide semiconductor (CMOS) sensor. Alternatively,each sensor of the array may be charged coupled device (CCD) sensor. Inanother embodiment, the sensor array may be made up of a combination ofCMOS and CCD sensors. The CCD sensor may comprise a photoactive regionand a transmission region for receiving and transmitting data whereasthe CMOS sensor may be made up of an integrated circuit having an arrayof pixel sensors. Each pixel may have a photodetector and an activeamplifier.

According to an embodiment, emitter 16 and detector 18 may be onopposite sides of a digit such as a finger or toe, in which case thelight that is emanating from the tissue has passed completely throughthe digit. In an embodiment, emitter 16 and detector 18 may be arrangedso that light from emitter 16 penetrates the tissue and is reflected bythe tissue into detector 18, such as a sensor designed to obtain pulseoximetry data from a patient's forehead.

In an embodiment, the sensor or sensor array may be connected to anddraw its power from monitor 14 as shown. In another embodiment, thesensor may be wirelessly connected to monitor 14 and include its ownbattery or similar power supply (not shown). Monitor 14 may beconfigured to calculate physiological parameters based at least in parton data received from sensor 12 relating to light emission anddetection. In an alternative embodiment, the calculations may beperformed on the monitoring device itself and the result of the oximetryreading may be passed to monitor 14. Further, monitor 14 may include adisplay 20 configured to display the physiological parameters or otherinformation about the system. In the embodiment shown, monitor 14 mayalso include a speaker 22 to provide an audible sound that may be usedin various other embodiments, such as for example, sounding an audiblealarm in the event that a patient's physiological parameters are notwithin a predefined normal range.

In an embodiment, sensor 12, or the sensor array, may be communicativelycoupled to monitor 14 via a cable 24. However, in other embodiments, awireless transmission device (not shown) or the like may be used insteadof or in addition to cable 24.

In the illustrated embodiment, pulse oximetry system 10 may also includea multi-parameter patient monitor 26. The monitor may be cathode raytube type, a flat panel display (as shown) such as a liquid crystaldisplay (LCD) or a plasma display, or any other type of monitor nowknown or later developed. Multi-parameter patient monitor 26 may beconfigured to calculate physiological parameters and to provide adisplay 28 for information from monitor 14 and from other medicalmonitoring devices or systems (not shown). For example, multiparameterpatient monitor 26 may be configured to display an estimate of apatient's blood oxygen saturation generated by pulse oximetry monitor 14(referred to as an “SpO₂” measurement), pulse rate information frommonitor 14 and blood pressure from a blood pressure monitor (not shown)on display 28.

Monitor 14 may be communicatively coupled to multi-parameter patientmonitor 26 via a cable 32 or 34 that is coupled to a sensor input portor a digital communications port, respectively and/or may communicatewirelessly (not shown). In addition, monitor 14 and/or multi-parameterpatient monitor 26 may be coupled to a network to enable the sharing ofinformation with servers or other workstations (not shown). Monitor 14may be powered by a battery (not shown) or by a conventional powersource such as a wall outlet.

FIG. 2 is a block diagram of a pulse oximetry system, such as pulseoximetry system 10 of FIG. 1, which may be coupled to a patient 40 inaccordance with an embodiment. Certain illustrative components of sensor12 and monitor 14 are illustrated in FIG. 2. Sensor 12 may includeemitter 16, detector 18, and encoder 42. In the embodiment shown,emitter 16 may be configured to emit at least two wavelengths of light(e.g., RED and IR) into a patient's tissue 40. Hence, emitter 16 mayinclude a RED light emitting light source such as RED light emittingdiode (LED) 44 and an IR light emitting light source such as IR LED 46for emitting light into the patient's tissue 40 at the wavelengths usedto calculate the patient's physiological parameters. In one embodiment,the RED wavelength may be between about 600 nm and about 700 nm, and theIR wavelength may be between about 800 nm and about 1000 nm. Inembodiments where a sensor array is used in place of single sensor, eachsensor may be configured to emit a single wavelength. For example, afirst sensor emits only a RED light while a second only emits an IRlight.

It will be understood that, as used herein, the term “light” may referto energy produced by radiative sources and may include one or more ofultrasound, radio, microwave, millimeter wave, infrared, visible,ultraviolet, gamma ray or X-ray electromagnetic radiation. As usedherein, light may also include any wavelength within the radio,microwave, infrared, visible, ultraviolet, or X-ray spectra, and thatany suitable wavelength of electromagnetic radiation may be appropriatefor use with the present techniques. Detector 18 may be chosen to bespecifically sensitive to the chosen targeted energy spectrum of theemitter 16.

In an embodiment detector 18 may be configured to detect the intensityof light at the RED and IR wavelengths. Alternatively, each sensor inthe array may be configured to detect an intensity of a singlewavelength. In operation, light may enter detector 18 after passingthrough the patient's tissue 40. Detector 18 may convert the intensityof the received light into an electrical signal. The light intensity isdirectly related to the absorbance and/or reflectance of light in thetissue 40. That is, when more light at a certain wavelength is absorbedor reflected, less light of that wavelength is received from the tissueby the detector 18. After converting the received light to an electricalsignal, detector 18 may send the signal to monitor 14, wherephysiological parameters may be calculated based on the absorption ofthe RED and IR wavelengths in the patient's tissue 40.

In an embodiment, encoder 42 may contain information about sensor 12,such as what type of sensor it is (e.g., whether the sensor is intendedfor placement on a forehead or digit) and the wavelengths of lightemitted by emitter 16. This information may be used by monitor 14 toselect appropriate algorithms, lookup tables and/or calibrationcoefficients stored in monitor 14 for calculating the patient'sphysiological parameters.

Encoder 42 may contain information specific to patient 40, such as, forexample, the patient's age, weight, and diagnosis. This information mayallow monitor 14 to determine, for example, patient-specific thresholdranges in which the patient's physiological parameter measurementsshould fall and to enable or disable additional physiological parameteralgorithms. Encoder 42 may, for instance, be a coded resistor whichstores values corresponding to the type of sensor 12 or the type of eachsensor in the sensor array, the wavelengths of light emitted by emitter16 on each sensor of the sensor array, and/or the patient'scharacteristics. In another embodiment, encoder 42 may include a memoryon which one or more of the following information may be stored forcommunication to monitor 14: the type of the sensor 12; the wavelengthsof light emitted by emitter 16; the particular wavelength each sensor inthe sensor array is monitoring; a signal threshold for each sensor inthe sensor array; any other suitable information; or any combinationthereof.

In an embodiment, signals from detector 18 and encoder 42 may betransmitted to monitor 14. In the embodiment shown, monitor 14 mayinclude a general-purpose microprocessor 48 connected to an internal bus50. Microprocessor 48 may be adapted to execute software, which mayinclude an operating system and one or more applications, as part ofperforming the functions described herein. Also connected to bus 50 maybe a read-only memory (ROM) 52, a random access memory (RAM) 54, userinputs 56, display 20, and speaker 22.

RAM 54 and ROM 52 are illustrated by way of example, and not limitation.Any suitable computer-readable media may be used in the system for datastorage. Computer-readable media are capable of storing information thatcan be interpreted by microprocessor 48. This information may be data ormay take the form of computer-executable instructions, such as softwareapplications, that cause the microprocessor to perform certain functionsand/or computer-implemented methods. Depending on the embodiment, suchcomputer-readable media may include computer storage media andcommunication media. Computer storage media may include volatile andnon-volatile, removable and non-removable media implemented in anymethod or technology for storage of information such ascomputer-readable instructions, data structures, program modules orother data. Computer storage media may include, but is not limited to,RAM, ROM, EPROM, EEPROM, flash memory or other solid state memorytechnology, CD-ROM, DVD, or other optical storage, magnetic cassettes,magnetic tape, magnetic disk storage or other magnetic storage devices,or any other medium which can be used to store the desired informationand which can be accessed by components of the system.

In the embodiment shown, a time processing unit (TPU) 58 may providetiming control signals to a light drive circuitry 60, which may controlwhen emitter 16 is illuminated and multiplexed timing for the RED LED 44and the IR LED 46. TPU 58 may also control the gating-in of signals fromdetector 18 through an amplifier 62 and a switching circuit 64. Thesesignals are sampled at the proper time, depending upon which lightsource is illuminated. The received signal from detector 18 may bepassed through an amplifier 66, a low pass filter 68, and ananalog-to-digital converter 70. The digital data may then be stored in aqueued serial module (QSM) 72 (or buffer) for later downloading to RAM54 as QSM 72 fills up. In one embodiment, there may be multiple separateparallel paths having amplifier 66, filter 68, and A/D converter 70 formultiple light wavelengths or spectra received.

In an embodiment, microprocessor 48 may determine the patient'sphysiological parameters, such as SpO₂ and pulse rate, using variousalgorithms and/or look-up tables based on the value of the receivedsignals and/or data corresponding to the light received by detector 18.Signals corresponding to information about patient 40, and particularlyabout the intensity of light emanating from a patient's tissue overtime, may be transmitted from encoder 42 to a decoder 74. These signalsmay include, for example, encoded information relating to patientcharacteristics. Decoder 74 may translate these signals to enable themicroprocessor to determine the thresholds based on algorithms orlook-up tables stored in ROM 52. User inputs 56 may be used to enterinformation about the patient, such as age, weight, height, diagnosis,medications, treatments, and so forth. In an embodiment, display 20 mayexhibit a list of values which may generally apply to the patient, suchas, for example, age ranges or medication families, which the user mayselect using user inputs 56.

The optical signal through the tissue can be degraded by noise, amongother sources. One source of noise is ambient light that reaches thelight detector. Another source of noise is electromagnetic coupling fromother electronic instruments. Movement of the patient also introducesnoise and affects the signal. For example, the contact between thedetector and the skin, or the emitter and the skin, can be temporarilydisrupted when movement causes either to move away from the skin. Inaddition, because blood is a fluid, it responds differently than thesurrounding tissue to inertial effects, thus resulting in momentarychanges in volume at the point to which the oximeter probe is attached.

Noise (e.g., from patient movement) can degrade a pulse oximetry signalrelied upon by a physician, without the physician's awareness. This isespecially true if the monitoring of the patient is remote, the motionis too small to be observed, or the doctor is watching the instrument orother parts of the patient, and not the sensor site. Processing pulseoximetry (i.e., PPG) signals may involve operations that reduce theamount of noise present in the signals or otherwise identify noisecomponents in order to prevent them from affecting measurements ofphysiological parameters derived from the PPG signals.

It will be understood that the present disclosure is applicable to anysuitable signals and that PPG signals are used merely for illustrativepurposes. Those skilled in the art will recognize that the presentdisclosure has wide applicability to other signals including, but notlimited to other biosignals (e.g., electrocardiogram,electroencephalogram, electrogastrogram, electromyogram, heart ratesignals, pathological sounds, ultrasound, or any other suitablebiosignal), dynamic signals, non-destructive testing signals, conditionmonitoring signals, fluid signals, geophysical signals, astronomicalsignals, electrical signals, financial signals including financialindices, sound and speech signals, chemical signals, meteorologicalsignals including climate signals, and/or any other suitable signal,and/or any combination thereof.

In one embodiment, a PPG signal may be transformed using a continuouswavelet transform. Information derived from the transform of the PPGsignal (i.e., in wavelet space) may be used to provide measurements ofone or more physiological parameters.

The continuous wavelet transform of a signal x(t) in accordance with thepresent disclosure may be defined as

$\begin{matrix}{{T\left( {a,b} \right)} = {\frac{1}{\sqrt{a}}{\int_{- \infty}^{+ \infty}{{x(t)}{\psi^{*}\left( \frac{t - b}{a} \right)}{\mathbb{d}t}}}}} & (9)\end{matrix}$where ψ*(t) is the complex conjugate of the wavelet function ψ(t), a isthe dilation parameter of the wavelet and b is the location parameter ofthe wavelet. The transform given by equation (9) may be used toconstruct a representation of a signal on a transform surface. Thetransform may be regarded as a time-scale representation. Wavelets arecomposed of a range of frequencies, one of which may be denoted as thecharacteristic frequency of the wavelet, where the characteristicfrequency associated with the wavelet is inversely proportional to thescale a. One example of a characteristic frequency is the dominantfrequency. Each scale of a particular wavelet may have a differentcharacteristic frequency. The underlying mathematical detail requiredfor the implementation within a time-scale can be found, for example, inPaul S. Addison, The Illustrated Wavelet Transform Handbook (Taylor &Francis Group 2002), which is hereby incorporated by reference herein inits entirety.

The continuous wavelet transform decomposes a signal using wavelets,which are generally highly localized in time. The continuous wavelettransform may provide a higher resolution relative to discretetransforms, thus providing the ability to garner more information fromsignals than typical frequency transforms such as Fourier transforms (orany other spectral techniques) or discrete wavelet transforms.Continuous wavelet transforms allow for the use of a range of waveletswith scales spanning the scales of interest of a signal such that smallscale signal components correlate well with the smaller scale waveletsand thus manifest at high energies at smaller scales in the transform.Likewise, large scale signal components correlate well with the largerscale wavelets and thus manifest at high energies at larger scales inthe transform. Thus, components at different scales may be separated andextracted in the wavelet transform domain. Moreover, the use of acontinuous range of wavelets in scale and time position allows for ahigher resolution transform than is possible relative to discretetechniques.

In addition, transforms and operations that convert a signal or anyother type of data into a spectral (i.e., frequency) domain necessarilycreate a series of frequency transform values in a two-dimensionalcoordinate system where the two dimensions may be frequency and, forexample, amplitude. For example, any type of Fourier transform wouldgenerate such a two-dimensional spectrum. In contrast, wavelettransforms, such as continuous wavelet transforms, are required to bedefined in a three-dimensional coordinate system and generate a surfacewith dimensions of time, scale and, for example, amplitude. Hence,operations performed in a spectral domain cannot be performed in thewavelet domain; instead the wavelet surface must be transformed into aspectrum (i.e., by performing an inverse wavelet transform to convertthe wavelet surface into the time domain and then performing a spectraltransform from the time domain). Conversely, operations performed in thewavelet domain cannot be performed in the spectral domain; instead aspectrum must first be transformed into a wavelet surface (i.e., byperforming an inverse spectral transform to convert the spectral domaininto the time domain and then performing a wavelet transform from thetime domain). Nor does a cross-section of the three-dimensional waveletsurface along, for example, a particular point in time equate to afrequency spectrum upon which spectral-based techniques may be used. Atleast because wavelet space includes a time dimension, spectraltechniques and wavelet techniques are not interchangeable. It will beunderstood that converting a system that relies on spectral domainprocessing to one that relies on wavelet space processing would requiresignificant and fundamental modifications to the system in order toaccommodate the wavelet space processing (e.g., to derive arepresentative energy value for a signal or part of a signal requiresintegrating twice, across time and scale, in the wavelet domain while,conversely, one integration across frequency is required to derive arepresentative energy value from a spectral domain). As a furtherexample, to reconstruct a temporal signal requires integrating twice,across time and scale, in the wavelet domain while, conversely, oneintegration across frequency is required to derive a temporal signalfrom a spectral domain. It is well known in the art that, in addition toor as an alternative to amplitude, parameters such as energy density,modulus, phase, among others may all be generated using such transformsand that these parameters have distinctly different contexts andmeanings when defined in a two-dimensional frequency coordinate systemrather than a three-dimensional wavelet coordinate system. For example,the phase of a Fourier system is calculated with respect to a singleorigin for all frequencies while the phase for a wavelet system isunfolded into two dimensions with respect to a wavelet's location (oftenin time) and scale.

The energy density function of the wavelet transform, the scalogram, isdefined asS(a,b)=|T(a,b)|²  (10)where ‘∥’ is the modulus operator. The scalogram may be rescaled foruseful purposes. One common rescaling is defined as

$\begin{matrix}{{S_{R}\left( {a,b} \right)} = \frac{{{T\left( {a,b} \right)}}^{2}}{a}} & (11)\end{matrix}$and is useful for defining ridges in wavelet space when, for example,the Morlet wavelet is used. Ridges are defined as the locus of points oflocal maxima in the plane. Any reasonable definition of a ridge may beemployed in the method. Also included as a definition of a ridge hereinare paths displaced from the locus of the local maxima. A ridgeassociated with only the locus of points of local maxima in the planeare labeled a “maxima ridge”.

For implementations requiring fast numerical computation, the wavelettransform may be expressed as an approximation using Fourier transforms.Pursuant to the convolution theorem, because the wavelet transform isthe cross-correlation of the signal with the wavelet function, thewavelet transform may be approximated in terms of an inverse FFT of theproduct of the Fourier transform of the signal and the Fourier transformof the wavelet for each required a scale and then multiplying the resultby √{square root over (a)}.

In the discussion of the technology which follows herein, the“scalogram” may be taken to include all suitable forms of rescalingincluding, but not limited to, the original unscaled waveletrepresentation, linear rescaling, any power of the modulus of thewavelet transform, or any other suitable rescaling. In addition, forpurposes of clarity and conciseness, the term “scalogram” shall be takento mean the wavelet transform, T(a,b) itself, or any part thereof. Forexample, the real part of the wavelet transform, the imaginary part ofthe wavelet transform, the phase of the wavelet transform, any othersuitable part of the wavelet transform, or any combination thereof isintended to be conveyed by the term “scalogram”.

A scale, which may be interpreted as a representative temporal period,may be converted to a characteristic frequency of the wavelet function.The characteristic frequency associated with a wavelet of arbitrary ascale is given by

$\begin{matrix}{f = \frac{f_{c}}{a}} & (12)\end{matrix}$where f_(c), the characteristic frequency of the mother wavelet (i.e.,at a=1), becomes a scaling constant and f is the representative orcharacteristic frequency for the wavelet at arbitrary scale a.

Any suitable wavelet function may be used in connection with the presentdisclosure. One of the most commonly used complex wavelets, the Morletwavelet, is defined as:ψ(t)=π^(−1/4)(e ^(t2πf) ⁰ ^(t) −e ^(−(2πf) ⁰ ⁾ ² ^(/2))e ^(−t) ²^(/2)  (13)where f₀ is the central frequency of the mother wavelet. The second termin the parenthesis is known as the correction term, as it corrects forthe non-zero mean of the complex sinusoid within the Gaussian window. Inpractice, it becomes negligible for values of f₀>>0 and can be ignored,in which case, the Morlet wavelet can be written in a simpler form as

$\begin{matrix}{{\psi(t)} = {\frac{1}{\pi^{1/4}}{\mathbb{e}}^{{\mathbb{i}2\pi}\; f_{0}t}{\mathbb{e}}^{{- t^{2}}/2}}} & (14)\end{matrix}$

This wavelet is a complex wave within a scaled Gaussian envelope. Whileboth definitions of the Morlet wavelet are included herein, the functionof equation (14) is not strictly a wavelet as it has a non-zero mean(i.e., the zero frequency term of its corresponding energy spectrum isnon-zero). However, it will be recognized by those skilled in the artthat equation (14) may be used in practice with f₀>>0 with minimal errorand is included (as well as other similar near wavelet functions) in thedefinition of a wavelet herein. A more detailed overview of theunderlying wavelet theory, including the definition of a waveletfunction, can be found in the general literature. Discussed herein ishow wavelet transform features may be extracted from the waveletdecomposition of signals. For example, wavelet decomposition of PPGsignals may be used to provide clinically useful information within amedical device.

Pertinent repeating features in a signal give rise to a time-scale bandin wavelet space or a rescaled wavelet space. For example, the pulsecomponent of a PPG signal produces a dominant band in wavelet space ator around the pulse frequency. FIGS. 3( a) and (b) show two views of anillustrative scalogram derived from a PPG signal, according to anembodiment. The figures show an example of the band caused by the pulsecomponent in such a signal. The pulse band is located between the dashedlines in the plot of FIG. 3( a). The band is formed from a series ofdominant coalescing features across the scalogram. This can be clearlyseen as a raised band across the transform surface in FIG. 3( b) locatedwithin the region of scales indicated by the arrow in the plot(corresponding to 60 beats per minute). The maxima of this band withrespect to scale is the ridge. The locus of the ridge is shown as ablack curve on top of the band in FIG. 3( b). By employing a suitablerescaling of the scalogram, such as that given in equation (11), theridges found in wavelet space may be related to the instantaneousfrequency of the signal. In this way, the pulse rate may be obtainedfrom the PPG signal. Instead of rescaling the scalogram, a suitablepredefined relationship between the scale obtained from the ridge on thewavelet surface and the actual pulse rate may also be used to determinethe pulse rate.

By mapping the time-scale coordinates of the pulse ridge onto thewavelet phase information gained through the wavelet transform,individual pulses may be captured. In this way, both times betweenindividual pulses and the timing of components within each pulse may bemonitored and used to detect heart beat anomalies, measure arterialsystem compliance, or perform any other suitable calculations ordiagnostics. Alternative definitions of a ridge may be employed.Alternative relationships between the ridge and the pulse frequency ofoccurrence may be employed.

As discussed above, pertinent repeating features in the signal give riseto a time-scale band in wavelet space or a rescaled wavelet space. For aperiodic signal, this band remains at a constant scale in the time-scaleplane. For many real signals, especially biological signals, the bandmay be non-stationary; varying in scale, amplitude, or both over time.FIG. 3( c) shows an illustrative schematic of a wavelet transform of asignal containing two pertinent components leading to two bands in thetransform space, according to an embodiment. These bands are labeledband A and band B on the three-dimensional schematic of the waveletsurface. In this embodiment, the band ridge is defined as the locus ofthe peak values of these bands with respect to scale. For purposes ofdiscussion, it may be assumed that band B contains the signalinformation of interest. This will be referred to as the “primary band”.In addition, it may be assumed that the system from which the signaloriginates, and from which the transform is subsequently derived,exhibits some form of coupling between the signal components in band Aand band B. When noise or other erroneous features are present in thesignal with similar spectral characteristics of the features of band Bthen the information within band B can become ambiguous (i.e., obscured,fragmented or missing). In this case, the ridge of band A may befollowed in wavelet space and extracted either as an amplitude signal ora scale signal which will be referred to as the “ridge amplitudeperturbation” (RAP) signal and the “ridge scale perturbation” (RSP)signal, respectively. The RAP and RSP signals may be extracted byprojecting the ridge onto the time-amplitude or time-scale planes,respectively. The top plots of FIG. 3( d) show a schematic of the RAPand RSP signals associated with ridge A in FIG. 3( c). Below these RAPand RSP signals are schematics of a further wavelet decomposition ofthese newly derived signals. This secondary wavelet decomposition allowsfor information in the region of band B in FIG. 3( c) to be madeavailable as band C and band D. The ridges of bands C and D may serve asinstantaneous time-scale characteristic measures of the signalcomponents causing bands C and D. This technique, which will be referredto herein as secondary wavelet feature decoupling (SWFD), may allowinformation concerning the nature of the signal components associatedwith the underlying physical process causing the primary band B (FIG. 3(c)) to be extracted when band B itself is obscured in the presence ofnoise or other erroneous signal features.

In some instances, an inverse continuous wavelet transform may bedesired, such as when modifications to a scalogram (or modifications tothe coefficients of a transformed signal) have been made in order to,for example, remove artifacts. In one embodiment, there is an inversecontinuous wavelet transform which allows the original signal to berecovered from its wavelet transform by integrating over all scales andlocations, a and b:

$\begin{matrix}{{x(t)} = {\frac{1}{C_{g}}{\int_{- \infty}^{\infty}{\int_{0}^{\infty}{{T\left( {a,b} \right)}\frac{1}{\sqrt{a}}{\psi\left( \frac{t - b}{a} \right)}\frac{{\mathbb{d}a}{\mathbb{d}b}}{a^{2}}}}}}} & (15)\end{matrix}$which may also be written as:

$\begin{matrix}{{x(t)} = {\frac{1}{C_{g}}{\int_{- \infty}^{\infty}{\int_{0}^{\infty}{{T\left( {a,b} \right)}{\psi_{a,b}(t)}\frac{{\mathbb{d}a}{\mathbb{d}b}}{a^{2}}}}}}} & (16)\end{matrix}$where C_(g) is a scalar value known as the admissibility constant. It iswavelet type dependent and may be calculated from:

$\begin{matrix}{C_{g} = {\int_{0}^{\infty}{\frac{{{\hat{\psi}(f)}}^{2}}{f}{\mathbb{d}f}}}} & (17)\end{matrix}$FIG. 3( e) is a flow chart of illustrative steps that may be taken toperform an inverse continuous wavelet transform in accordance with theabove discussion. An approximation to the inverse transform may be madeby considering equation (15) to be a series of convolutions acrossscales. It shall be understood that there is no complex conjugate here,unlike for the cross correlations of the forward transform. As well asintegrating over all of a and b for each time t, this equation may alsotake advantage of the convolution theorem which allows the inversewavelet transform to be executed using a series of multiplications. FIG.3( f) is a flow chart of illustrative steps that may be taken to performan approximation of an inverse continuous wavelet transform. It will beunderstood that any other suitable technique for performing an inversecontinuous wavelet transform may be used in accordance with the presentdisclosure.

FIG. 4 is an illustrative continuous wavelet processing system 400 thatmay include a wavelet transform viewer in accordance with someembodiments. In this embodiment, one or more input signal generators 410each generate one or more input signal 416. As illustrated, input signalgenerator 410 a may include oximeter 420 coupled to sensor 418, whichmay provide as input signal 416 a, a PPG signal. It will be understoodthat input signal generators 410 may include any suitable signalsources, signal generating data, signal generating equipment, or anycombination thereof to produce signals 416. Signals 416 may be anysuitable signals, such as, for example, biosignals (e.g.,electrocardiogram, electroencephalogram, electrogastrogram,electromyogram, heart rate signals, pathological sounds, ultrasound, orany other suitable biosignal), dynamic signals, non-destructive testingsignals, condition monitoring signals, fluid signals, geophysicalsignals, astronomical signals, electrical signals, financial signalsincluding financial indices, sound and speech signals, chemical signals,meteorological signals including climate signals, and/or any othersuitable signal and/or any combination thereof.

In this embodiment, signals 416 may be coupled to processor 412.Processor 412 may be any suitable software, firmware, and/or hardware,and/or combinations thereof for processing signal 416. For example,processor 412 may include one or more hardware processors (e.g.,integrated circuits), one or more software modules, computer-readablemedia such as memory, firmware, or any combination thereof. Processor412 may, for example, be a computer or may be one or more chips (i.e.,integrated circuits). Processor 412 may perform the calculationsassociated with the continuous wavelet transforms of the presentdisclosure as well as the calculations associated with any suitableinterrogations of the transforms. Processor 412 may perform any suitablesignal processing of signals 416 to filter signals 416, such as anysuitable band-pass filtering, adaptive filtering, closed-loop filtering,and/or any other suitable filtering, and/or any combination thereof.

Processor 412 may be coupled to one or more memory devices (not shown)or incorporate one or more memory devices such as any suitable volatilememory device (e.g., RAM, registers, etc.), non-volatile memory device(e.g., ROM, EPROM, magnetic storage device, optical storage device,flash memory, etc.), or both. The memory may be used by processor 412to, for example, store data corresponding to a continuous wavelettransform of input signals 416, such as data representing a scalogram.In one embodiment, data representing a scalogram may be stored in RAM ormemory internal to processor 412 as any suitable three-dimensional datastructure such as a three-dimensional array that represents thescalogram as energy levels in a time-scale plane. Any other suitabledata structure may be used to store data representing a scalogram.

Processor 412 may be coupled to wavelet transform viewer 414. Wavelettransform viewer 414 may be integrated with or used in combination withany suitable output device such as, for example, one or more medicaldevices (e.g., a medical monitor that displays various physiologicalparameters, a medical alarm, or any other suitable medical device thateither displays physiological parameters or uses the output of processor412 as an input), one or more display devices (e.g., monitor, PDA,mobile phone, any other suitable display device, or any combinationthereof), one or more audio devices, one or more memory devices (e.g.,hard disk drive, flash memory, RAM, optical disk, any other suitablememory device, or any combination thereof), one or more printingdevices, any other suitable output device, or any combination thereof.

It will be understood that system 400 may be incorporated into system 10(FIGS. 1 and 2) in which, for example, an input signal generator 410 maybe implemented as parts of sensor 12 and monitor 14 and processor 412may be implemented as part of monitor 14.

Control input 428 may be coupled to processor 412 and may be used tocontrol the operation of processor 412 and wavelet transform viewer 414.In some embodiments control input 428 may be coupled directly to wavelettransform viewer 414 (not shown). Control input 428 may be any suitableuser interface, such as a remote control, mouse, trackball, keypad,keyboard, touch screen, touch pad, stylus input, joystick, voicerecognition interface, or other user input interfaces.

The present disclosure relates to a wavelet transform viewer fordisplaying signals, such as physiological signals (e.g., a PPG signal)simultaneously with a wavelet plot of at least one of those signals. Forexample, the wavelet transform viewer may simultaneously display a PPGsignal and a wavelet transform generated from the PPG signal. Thewavelet transform viewer may allow a particular portion of thephysiological signal to be selected such that the displayed wavelettransform can be generated for the selected portion of the physiologicalsignal. This selected portion may be an area of interest on thephysiological signal and thus the wavelet transform scalogram generatedfrom this selected area may provide additional information relating tothe area of interest.

The wavelet transform viewer may be part of a physiological monitoringsystem (e.g., a PSG) that can simultaneously display multiplephysiological signals and physiological parameters including, forexample, ECG signals, EEG signals, EOG signal, and EMG signals. Thesesignals may be displayed within the viewer simultaneously with at leastone wavelet plot generated from a selected portion of one of thesignals.

FIG. 5 shows an illustrative display 500 of a wavelet transform viewerin accordance with embodiments. Display 500 includes large signal plot510 of a signal plotted over time. The signal may be a PPG signal or anyother suitable signal. Selection box 515 may be used to select a portionof the signal from large signal plot 510. Selected signal plot 520 is aplot of the selected portion of the signal. Wavelet plot 530 is a plotof a wavelet transform generated from the selected portion of thesignal. In some embodiments, wavelet plot 530 may be a wavelet scalogramplot. Wavelet plot 530 may include pulse band 531, respiration band 532,and individual pulse features 533. In particular, the pulse may be shownas band 531 across the scalogram in the modulus plot with individualpulse features 533 becoming apparent at smaller scales as the wavelettransform resolves the intra-pulse morphology at these scales.

In addition to a scalogram plot of the wavelet transform modulus values(and multiples thereof), other wavelet transform plots can be providedin the wavelet transform viewer including the phase of the transform,real or imaginary parts of the transform, and cross-correlations betweenthe signal and other signals and their transforms. For example, FIG. 6shows an illustrative wavelet transform viewer that includes a wavelettransform plot of the real parts of the transform with pulse band 631and respiration band 632, FIG. 7 shows an illustrative wavelet transformviewer that includes a wavelet transform plot of the imaginary parts ofthe transform with pulse band 731 and respiration band 732, and FIG. 8shows an illustrative wavelet transform viewer that includes a wavelettransform plot of the phase of the transform with pulse band 831,respiration band 832, pulse cycle “beat period” 834, and respirationcycle “breath period” 835 in accordance with embodiments. The real andimaginary transform plots (FIGS. 6-7) may show the oscillatory nature ofthe pulse and features. In addition, the cycling of respiratory activitycan be see at lower scales. The phase plot (FIG. 8) also shows theregular cycling of phase at the pulse and respiratory scales. Theregular cycling of the pulse and respiratory activity are indicative ofthe heart beat period and breath period respectively. The phase plot isalso useful in visualizing marked changes in phase relationships withinthe signal.

Returning to FIG. 5, the time scale of selected signal plot 520 may besmaller than the time scale of large signal plot 510. In other words,large signal plot 510 may display the signal over a relatively longertime period and selected signal plot 520 may show the selected portionof the signal over a relatively shorter time period. Displaying theselected portion of the signal in this manner may allow the selectedportion of the signal to be viewed and examined in greater detail withinselected signal plot 520 than within large signal plot 510. Selectedsignal plot 520 and wavelet plot 530 may be displayed with substantiallysimilar time scales and may correspond to approximately the sameselected portion of the signal.

Wavelet plot 530 may also aid in signal interpretation. As discussedabove, computing a wavelet transform of the signal and displaying awavelet plot of the transformed signal may reveal information that maynot be readily observed from the signal itself. For example, a scalogramof a selected portion of a PPG signal may provide pulse and other heartrate information. As another example, a scalogram of a selected portionmay provide respiratory information such as respiration rate,respiration effort, and changes in respiratory activity. Suchrespiration activity as interpreted from the wavelet transform plot mayaid in the diagnosis of, for example, apnea type. As yet anotherexample, a scalogram of a selected portion may provide information onlarge scale signal artifact due to, for example, movement or vasomotion.Vasomotion may, for example, be indicative of sleep arousal.

According to embodiments, if an area of interest is identified withinlarge signal plot 510, the area can be selected using selection box 515.The selected portion of the signal may then be simultaneously displayedin selected signal plot 520 and wavelet plot 530. Selection box 515 mayselect any portion of large signal plot 510, including portions of largesignal plot that are out of the range of the viewer. Selection box maybe moved along the time axis of large signal plot using selection slider540. Selection slider 540 may be moved left and right using any suitableuser interface such as control input 428 (FIG. 4). Similarly, controlinput 428 also may be used to directly select a particular portion oflarge signal plot 510. Finally, control input 428 may also be used toinput a time that may approximately correspond to a desired start-point,end-point, or mid-point for selection box 515. Additionally, automatedselection of portion to be viewed may be achieved by, for example,automatically zooming into identified regions of interest (e.g., areasof apnea).

The size of selection box 515 may also be adjusted to set the size ortime span of the signal portion to be selected. For example, the size ofselection box 515 may be increased or decreased by selecting and movingeither of the edges of selection box 515 using control input 428. Alarger period may be selected when viewing longer period events orsequence of events and shorter periods may be selected when viewingtemporally localized events. Alternatively, control input 428 may beused to select the size or time span of selection box 515 from severalpre-determined sizes or may be used to enter a desired size or timespan.

After the portion of the signal is selected, a wavelet transform of theselected portion of the signal may be calculated and a wavelet plot maybe generated from the transformed signal. When the selection is changedor adjusted, a new wavelet transform may be computed and a new waveletplot may be generated. Wavelet transforms may be calculated for anentire signal. However, signals tend to be very long and it may be verycomputationally expensive to perform a high resolution wavelet transformon an entire signal. Therefore, in accordance with embodiments, thewavelet transform may be calculated after a signal portion is selectedand the resolution of the transform may be optimized accordingly (e.g.,by sub-sampling the sampling time and scales as appropriate for viewingpurposes).

Although only one signal (e.g., a PPG signal) is shown in display 500,it should be understood that wavelet transform viewer 414 may supportthe simultaneous display of multiple signals. For example, wavelettransform viewer 414 may be used to display the output of apolysomnograph (PSG) for use in monitoring a group of physiologicalchanges that occur during sleep. A PSG typically monitors PPG signals,EEG signals, ECG signals, EOG signal, EMG signals, and any othersuitable signal. Some or all of these monitored signals may besimultaneously displayed in wavelet transform viewer 414. The monitoredsignals may be simultaneously displayed on individual large signal plotsor grouped together in several large scale plots with some signals beingplotted on the same set of axes.

When multiple signals are displayed within wavelet transform viewer 414one or more selected signal plots and wavelet plots may besimultaneously displayed. In some embodiments only one selected signalplot and one wavelet plot are displayed. The selected signal plot andthe wavelet plot may correspond to a particular signal (e.g., a PPGsignal) or may be configured to correspond to any of several signals.For example, the selected signal and wavelet plots may be set tocorrespond to either a PPG signal or an EEG signal. Alternatively,multiple selected signal plots and wavelet plots may be provided for thesimultaneous display of multiple signals. In some embodiments, one ormore of the wavelet plots may be displayed without a correspondingselected signal plots. This may free space within wavelet transformviewer 414 for additional signal and wavelet plots.

FIG. 9 is a flowchart of an illustrative process for generating awavelet transform viewer display in accordance with an embodiment.Process 900 may begin at step 902. At step 904, a first portion of asignal is displayed. For example, the first portion of the signal may bedisplayed within large signal plot 510 of FIG. 5. The signal may be aPPG signal, another physiological signal, or any other suitable signal.At step 906, a second portion of the signal is selected. In anembodiment, the second portion of the signal may selected from withinthe first portion of the signal. The location and size of the secondportion of the signal may be adjustable. The selection may be mademanually using control input 428 or automatically using processor 412(FIG. 4).

Process 900 may advance to step 908, in which the second portion of thesignal is transformed using a wavelet transform. At step 910 a waveletplot is generated based on the transformed signal. The wavelet plot maybe a wavelet scalogram as show in FIG. 5 or may be a wavelet plot thatis based on any other suitable wavelet transform including the phase ofthe transform, real or imaginary parts of the transform, andcross-correlations between the signal and other signals and theirtransforms. Then, at step 912 the wavelet plot is simultaneouslydisplayed with the signal. The wavelet plot may be simultaneouslydisplayed with the first portion of the signal, with the second portionof the signal or with any suitable portion of the signal. As show inFIG. 5, the wavelet plot may simultaneously displayed with both thefirst and the second portion of the signal.

Process 900 may then advance to step 914, to determine whether theselection of the second portion has been modified. The selection of thesecond portions may be modified in order to display a wavelet plot of adifferent portion of the signal. The selection of the second portion mayalso be modified in order to adjust the current selection, for example,by adjusting the start point, end point, or duration of the selection.The modification may be made manually using control input 428 orautomatically using processor 412 (FIG. 4). If the second portion hasbeen modified, steps 908-914 may be repeated to transform the modifiedportion, generate a wavelet plot based on the transformed signal, andsimultaneously display the wavelet plot with the signal. If the secondportion has not been modified, process 900 may then advance to step 916and end.

The foregoing is merely illustrative of the principles of thisdisclosure and various modifications can be made by those skilled in theart without departing from the scope and spirit of the disclosure. Thefollowing claims may also describe various aspects of this disclosure.

1. A method for displaying a signal in a wavelet transform viewer, themethod comprising: receiving a signal in a processor; receiving a userselection of a portion of the signal corresponding to an area ofinterest via control input; transforming the selected portion of thesignal using a wavelet transform using the processor to generate atransformed signal; generating a wavelet plot based on the transformedsignal using the processor; and displaying the wavelet plotsimultaneously with a plot of the selected portion of the signal on adisplay.
 2. The method of claim 1 wherein the signal comprises aphotoplethysmographic (PPG) signal.
 3. The method of claim 1 wherein thewavelet plot comprises a continuous wavelet scalogram of the transformedsignal.
 4. The method of claim 1 wherein the wavelet plot comprises aplot of a phase of the transformed signal, a real part of thetransformed signal, an imaginary part of the transformed signal, and/ora cross-correlation between the transformed signal and a second signal,and/or combinations thereof.
 5. The method of claim 1 wherein theselected portion of the signal is adjustable.
 6. The method of claim 1further comprising displaying a plot of the received signalsimultaneously with the plot of the selected portion of the signal andthe wavelet plot.
 7. The method of claim 1 further comprising: receivinga selection of a second portion of the signal; transforming the selectedsecond portion of the signal using a wavelet transform to generate afurther transformed signal; regenerating the wavelet plot based on thefurther transformed signal; and replacing the displayed wavelet plotwith the regenerated wavelet plot.
 8. The method of claim 1 furthercomprising displaying at least one other signal plot with the waveletplot and the plot of the selected portion of the signal.
 9. The methodof claim 1 further comprising displaying a wavelet plot of at least oneother signal.
 10. The method of claim 1 further comprising displayingthe wavelet plot with the plot of the selected portion of the signalwithin a polysomnograph (PSG) display.
 11. A wavelet transform viewercomprising: a processor capable of: receiving a signal; receiving a userselection of a portion of the signal corresponding to an area ofinterest; transforming the selected portion of the signal using awavelet transform to generate a transformed signal; generating a waveletplot based on the transformed signal; and a display capable ofdisplaying the wavelet plot simultaneously with a plot of the selectedportion of the signal.
 12. The wavelet transform viewer of claim 11wherein the signal comprises a photoplethysmographic (PPG) signal. 13.The wavelet transform viewer of claim 11 wherein the wavelet plotcomprises a continuous wavelet scalogram of the transformed signal. 14.The wavelet transform viewer of claim 11 wherein the wavelet plotcomprises a plot of a phase of the transformed signal, a real part ofthe transformed signal, an imaginary part of the transformed signal,and/or a cross-correlation between the transformed signal and a secondsignal, and/or combinations thereof.
 15. The wavelet transform viewer ofclaim 11 further comprising a control input capable of selecting and/oradjusting the selected portion of the signal.
 16. The wavelet transformviewer of claim 11 wherein the display is further capable of displayinga plot of the received signal with the plot of the selected portion ofthe signal and the wavelet plot.
 17. The wavelet transform viewer ofclaim 11 the processor further capable of: receiving a selection of asecond portion of the signal; transforming the selected second portionof the signal using a wavelet transform to generate a furthertransformed signal; regenerating the wavelet plot based on the furthertransformed signal; and replacing the displayed wavelet plot with theregenerated wavelet plot.
 18. The wavelet transform viewer of claim 11wherein the display is further capable of displaying at least one othersignal plot with the wavelet plot and the plot of the selected portionof the signal.
 19. The wavelet transform viewer of claim 11 wherein thedisplay is further capable of displaying a wavelet plot of at least oneother signal.
 20. The wavelet transform viewer of claim 11 wherein thedisplay comprises a polysomnograph (PSG) display.
 21. Computer-readablemedium for use in displaying a signal in a wavelet transform viewer, thecomputer-readable medium having computer program instructions recordedthereon for: receiving a signal; receiving a user selection of a portionof the signal corresponding to an area of interest; transforming theselected portion of the signal using a wavelet transform to generate atransformed signal; generating a wavelet plot based on the transformedsignal; and displaying the wavelet plot simultaneously with a plot ofthe selected portion of the signal.